Who should be the greatest - See on Matthew 18:1-5 (note).

But they held their peace,.... Fearing a reprimand, for their vanity and affectation of worldly grandeur:
for by the way they had disputed among themselves, who should be the greatest; that is, who should be advanced to the highest post, and have the greatest place of authority, honour, and dignity, in the temporal kingdom of the Messiah, they expected would be in a little time set up; for notwithstanding what Christ had said to them, concerning his being given up to the power of men, and concerning his death and resurrection, they still retained their former principle, to which they knew not how to reconcile his dying; and therefore chose rather to leave his meaning in suspense, and remain ignorant about it, than quit so darling a notion: and doubtless this dispute was occasioned by what Christ had said to them; who afterwards, getting by themselves, talked about it, which led on to a warm contest, about precedence in his kingdom.

But they held their peace: for by the way they had disputed among themselves, who should be the greatest--From Matthew 18:1 we should infer that the subject was introduced, not by our Lord, but by the disciples themselves, who came and asked Jesus who should be greatest. Perhaps one or two of them first referred the matter to Jesus, who put them off till they should all be assembled together at Capernaum. He had all the while "perceived the thought of their heart" (Luke 9:47); but now that they were all together "in the house," He questions them about it, and they are put to the blush, conscious of the temper towards each other which it had kindled. This raised the whole question afresh, and at this point our Evangelist takes it up. The subject was suggested by the recent announcement of the Kingdom (Matthew 16:19-28), the transfiguration of their Master, and especially the preference given to three of them at that scene.

Who should be greatest - Prime minister in his kingdom.